Mathematical modelling of dynamical systems plays an important role in many branches of science. Since the second half of the last century dynamical systems and differential geometry have developed into a mathematical discipline with an ever-growing impact on the construction of mathematical models in different applied sciences. In particular, geometric mechanics has become the common name that is given to those research activities that are devoted to the application of these research areas in various fields such as classical mechanics (Newtonian, Lagrangian and Hamiltonian mechanics), control theory and continuum mechanics. Using tools and techniques of Riemann geometry, contact geometry, symplectic and Poisson geometry, and exploiting the properties of Lie groups, fiber bundles, connections, distributions, etc., geometric mechanics has contributed a lot to the description and analysis of the structure and properties of mechanical systems, impacting in many fields for engineering applications, theoretical physics, fluids dynamics and material sciences.

Prof. Anthony Bloch received his Ph.D from Harvard University in 1985 and has received a Presidential Young Investigator Award and a Guggenheim Fellowship among other awards. He has held various visiting positions and was a member of the Institute for Advanced Studies in Princeton. He serve on the editorial boards of a number of journals in dynamics and control.

His research includes work on the geometry and dynamics of finite and infinite dimensional integrable Hamiltonian systems, work on the geometry and dynamics of nonholonomic systems and work on the dynamics and control of nonlinear systems particularly those arising in mechanics. He is currently working on applications to quantum mechanics and biology including connections between neuroscience and locomotion.

The workshop will be divided into the different aspects of mathematical modelling and its role on sciences. The three fundamental stones are:

  • Dynamical Systems (Integrable systems, Hamiltonian systems, new results for qualitative aspects of dynamical systems, celestial mechanics and the many-body problem, ergodic theory ...)
  • Control Theory (Geometric control, stabilization of control systems, optimal control, safety conditions, mathematical analysis of control systems, quantum control, distributed control, robotics applications, ...)
  • Geometric Mechanics (Geometric Integration, Reduction by symmetries, nonholonomic systems, stochastic mechanics, fluid dynamics, applications in material sciences and continuum mechanics; symplectic, cosymplectic and contact geometry ...)